Scale Space

In this paper, we explain why Scale Space theories do not incorporate obvious restrictions imposed by the physics of image generation [20]. The heat equation (linear scale space) is not contrast invariant and destroys Tjunctions [12]. The same is true for the recently proposed curvature equations (mean curvature motion [2] and a ne shortening [27] [2]) : They break the symmetry of junctions [4]. To apply directly these models to natural world images, with occlusions, is therefore impossible. Returning to the original problem of scale space, we show how level lines can be found in an image without smoothing. This makes useless the recourse to a spurious parameter like scale to detect edges. Dep. of Mathematics and Informatics, University of Illes Balears, 07071 Palma de Mallorca, Spain, [email protected] Dep. of Mathematics and Informatics, University of Illes Balears, 07071 Palma de Mallorca, Spain, [email protected] CEREMADE, Universite Paris-Dauphine, Place du Marechal Lattre de Tassigny, 75775 Paris Cedex 16, France, [email protected]